Curriculum vitae

22.05.1976 I was born.

01.09.1993 Entered the Mechanics and Mathematics Department of the Novosibirsk State University.

1997 Graduated from MMD NSU, entered the second level (magister degree) of MMD NSU.

1998 Began to teach algebra for the first year students of MMD NSU.

1999 Graduated from the second level (magister degree) of MMD NSU, became a PhD student of the S.L.Sobolev's Institute of Mathematics SB RAS.

2000 Awarded kandidate of phisics and mathematics degree (PhD degree in phisics and mathematics), the title of the thesis is "Abelian and nilpotent subgroups of maximal order of finite simple groups".

01.01.2001-31.08.2001 Began to work in IM SB RAS as a high engineer, than as a senior research fellow.

01.09.2001-31.05.2004 Post-Doctoral grant in the University of Padua (Italy). Worked with Professor Federico Menegazzo and Professor Maria Clara Tamburini.

01.06.2004-present I work in IM SB RAS as a senior research fellow (now as a deputy director), teach algebra for the first year students of MMD NSU, and give lectures on “Number Theory” for six-year students and on “Linear algebraic groups" for students and PhD-students of algebra and logic chair.

2007 Awarded Doctor of phisics and mathematics, the title of the thesis is "Carter subgroups of finite groups".

5 recent conferences:

1.      Asymptotic group theory, 17-21 August, 2015, Renyi Institute, Budapest, Hungary.

2.      The International Conference and PhD Summer School «Groups and Graphs, Algorithms and Automata»,09-15 August, Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia.

3.      International Conference on Groups and Algebras, dedicated to the 100-th birthday celebration for late Professor Hsio-fu Tuan, 24-30 June, 2014, Peking University,  Beijing, China.

4.      Groups St Andrews 2013 in St Andrews, 3-11, August, 2013, University of St.Andrews, Great Britain.

5.      The International Conference on Group Theory in Honor of the 70th Birthday of Professor Victor D. Mazurov. 16-20 July, 2013, Sobolev Institute of Mathematics, Novosibirsk, Russia.

Main results

1.      In all finite simple groups the structure and orders of abelian and nilpotent subgroups of maximal order are found.

2.      It is proven that if a finite group possessing a nilpotent subgroup of index n, then the index of its Fitting subgroup is not greater than n^9.

3.      For a finite group of Lie type G over a field of characteristic p there exists a constant c such that the number of subgroups with trivial normal p-subgorup of G is not greater than |G|^c, while the number of subgroups of G is not less than |G|^{(log_q|G|)/16}, where q is the order of the definition field of  G.

4.      It is proven that a complete analogue of Sylow theorem for pi-Hall subgroups of a finite group is satisfied if and only if it is satisfied in each composition factor of the group. (with D.O.Revin).

5.      It is proven that Carter subgroups of a finite group are conjugate (with M.C.Tamburini). Moreover, an existence criterion for Carter subgroups of finite groups is obtained.

6. It is proven that every finite $\pi$-solvable group possesses three $\pi$-Hall subgroups whose intersection equals $\pi$-radical.

7.      The structure and main invariants for prime graphs of all finite simple groups are found (with A.V.Vasil’ev).

8. We (together with A.A.Gal’t) complete the classification of simple strongly real groups.
9. The classification of admissible abelian groups of automorphisms for NHDM and of admissible finite groups of automorphisms for 3HDM is obtained (with I.P.Ivanov).